Distribution of risk score

The lasso.results object is a list with multiple plots and tables. We start with the observation of the risk score generated, its refit as a predictor in a Cox proportional hazard model, and the cross-validated concordance index distribution.

lasso.results$RiskHistogram

lasso.results$RiskScoreSummary

##            Lower 10% 1st Quarter 1st Tertile Median 2nd Tertile
## Risk Score      2.54        4.04        4.39   5.62        6.16
##            3rd Quarter Upper 10%
## Risk Score        6.36      7.93

kable(summary(lasso.results$RiskRefit)$coefficients)

lasso.results$ciSummary

## NULL

The histogram shows the distribution of the composite risk score computed for each patients. This was rescaled from 0 to 10 for ease of interpretation. The median concordance index for the OncoCast score for predicting survival is 0.78.

Feature Selection

In order to explore feature selection two plots are available, the first is a simple bar plot of the selection frequency of the most frequently selected features. The second has more details, it lets the user interactively explore the selection and coefficients of all the features at once. As the user hovers over the points the name of the gene represented by that point along with the average hazard for a mutation on that gene.

lasso.results$inflPlot

## NULL

lasso.results$selectInflPlot

As expected we observe on the bar plot that the features that were simulated to be associated with the outcome have been selected 100% of the time.

The volcano plot shows the frequency at which each feature was selected in the 100 splits we have generated by the mean penalized coefficients found in the cross-validation. Note that the size and color of the points are linked to the mutation frequency of each feature. We observe now that not only do the important covariates have higher selection frequency but also much larger coefficient values.

Survival Stratification

As mentioned above the numGroups argument will enable the user to create between 2 to 4 groups that are made by making specified cuts (using the cuts argument) in the averaged predicted risk score. In this example we made four groups with cuts at 25th, 50th and 75th percentile. For example, the first group corresponds to the patients in the lowest quartile of the predicted risk score (0 <= predicted risk score <= 4.15). We can check how distinct the groups are in survival using a Kaplan-Meier plot as shown below.

lasso.results$KM

Mutational profiles per groups

Furthermore two other tools contained in the output of this function let us explore the distribution of features per group generated. Note that this is only possible with binary data at the moment. The first plot is simple bar plot of the frequency of feature events for the most frequently selected predictors per group.

lasso.results$mut_Plot

In order to explore the combinations of genes in each risk group, getResults_OC function returns a second interactive plot. It is a multiple pie chart plot where each pie represents a risk group (in increasing order of risk). As the user hovers over different slices of the pies the name of the mutated genes and gene combinations in that profile along with the number of patients showing that profile and the proportion of patients in that risk group they represent.

To ensure that the number different possible profiles is not too high and ensure that the plot remains readable we limit to the use of the top five most frequently selected genes. The user can also specify the features to be used to generate the pie chart by inputting a character vector containing the exact names of the features into the geneList argument (which is defaulted to be the top 5 most frequently selected genes).

lasso.results$PieChart

## NULL

As an example, if the user hovers on the pie chart for the high risk group (far right) and on the dark red slice, it shows that 21 patients (or 28%) in the high risk group have the ImpCov2 and ImpCov3 combination.

Prediction module

The last available function in the package enables the user to input a set of new patient data with the same set of features in the original patient set used for training the risk model and retrieve the predicted genetic risk score for the new subjects.

set.seed(3)
new.data <- as.data.frame(matrix(rbinom(10*100,1,0.5),nrow=100,ncol = 10))
colnames(new.data) <- c("ImpCov1","ImpCov2","ImpCov3","ImpCov4","ImpCov5","Cov6","Cov7",
                        "Cov8","Cov9","Cov10")
rownames(new.data) <- paste0("Incoming",1:100)
Incoming <- predIncomingSurv(Out$LASSO,new.data,surv.print = c(5,10,15),riskRefit = lasso.results$RiskRefit)

Here are the different objects outputted by this function, first a data frame of the new patients data with an added column containing the predicted genetic risk score for those patients.

head(Incoming$data.out)

##           ImpCov1 ImpCov2 ImpCov3 ImpCov4 ImpCov5 Cov6 Cov7 Cov8 Cov9
## Incoming1       0       1       1       0       0    0    0    0    1
## Incoming2       1       1       1       0       1    0    1    1    1
## Incoming3       0       0       0       1       1    1    1    1    1
## Incoming4       0       1       0       1       1    0    1    1    0
## Incoming5       1       1       1       1       1    1    0    1    1
## Incoming6       1       0       0       1       0    1    0    1    1
##           Cov10 OncoCastRiskScore
## Incoming1     1          6.496929
## Incoming2     0          5.944741
## Incoming3     0          1.528109
## Incoming4     1          3.327332
## Incoming5     1          4.368665
## Incoming6     0          5.985917

Second is a histogram showing the distribution of those predicted genetic risk scores.

Incoming$RiskHist

An interactive survival plot of individual patients selected using the surv.print function. As the user hovers over the different points extra information will be displayed.

Incoming$IncKM

Note that the user can select which predicted survival curves will be displayed in the above graph using the surv.print argument.

Validation module

If the user has access to an alternative dataset with survival information a validation can be performed. Where the trained model will be applied to the validation data and stratification will be performed based on the choices made previously. Say for example that the data in the section above did have survival information:

# add time component
coefs <- c(1.2,1.3,-1.5,-1,-1,rep(0,ncol(new.data)-5))
mu <- as.vector(coefs %*% t(new.data))
n = nrow(row(new.data))
time <- rexp(n,exp(mu))*12
c <- runif(n,0,as.numeric(quantile(time,0.8)))
status <- ifelse(time < c , 1,0)
time <-pmin(time,c)
new.data$time <- time
new.data$status <- status

Then the validation can be called in the following manner:

validation <- validate(OC_object=Out$LASSO,Results=lasso.results,
in.data=new.data, formula=Surv(time,status)~.)

Note the necessity here to have the formula as input. The validation function similarly returns a histogram of the risk distribution:

validation$RiskHistogram.new

A data frame of the data used including the predicted risk and the associated risk group:

validation$out.data[1:10,c("OncoCastRiskScore","RiskGroup")]

##            OncoCastRiskScore RiskGroup
## Incoming1           6.496929         4
## Incoming2           5.944741         3
## Incoming3           1.528109         1
## Incoming4           3.327332         1
## Incoming5           4.368665         2
## Incoming6           5.985917         3
## Incoming7           2.432940         1
## Incoming8           2.527679         1
## Incoming9           4.600675         2
## Incoming10          3.597878         1

And a Kaplan-Meier plot with the cuts chosen initially:

validation$KM

Left-truncated Survival analysis

The OncoCast function also allows the user to perform a left-truncated survival analysis. A simple change in the formula argument will suffice to do this. Taking a simple example with the survData.LT data included in the package, the time and status variables are named time1 (for the late-entry time), time2 (for the survival time) and status (for the censoring). An example of such data can be found in the ‘survData.LT’ set.

head(survData.LT[,1:5]) 

##                 time1       time2 status ImpCov1 ImpCov2
## Patient 1  0.02966663   3.0503361      1       0       1
## Patient 2 16.84681767  50.0844402      1       1       0
## Patient 3  0.24815977   0.9974178      1       1       0
## Patient 4 37.88561581  45.7715850      1       0       0
## Patient 5  7.53586627 100.0087122      0       0       0
## Patient 6  0.13734736   1.7932666      1       1       1

The user simply needs to use the argument : formula = Surv(time1,time2,status~.)

Launching the app

In order to launch the app the user will need to input the following line in the console (after loading the OncoCast package):

# launchApp()

Note that this cannot be run in markdown and thus is commented out. The following will be screenshots of what the app looks like. After the command above is ran a new window will open asking for two files:

• a saved OncoCast run containing a single method (this file will be generated automatically when using the ‘save = T’ argument in the OncoCast() function).

• the data corresponding to that specific run. Note that if the data does not match the app will crash. The data must be loaded as a comma separated value file with rownames as the first column.

Such files can be found in the ‘Test’ folder of the package on github https://github.com/AxelitoMartin/OncoCast. Namely here I will be using the OncoCast run ‘appTest_LASSO.Rdata’ and the data ‘appTest_data.csv’ (which correspond to the results shown above).

Once the app performs the data checks the other tabs will become functional.

Viewing the results

The ‘Dashboard’ tab will cover the prognostics of our model with all the necessary information to make an optimal decision on the cuts to be performed. This tab will show the distribution of the risk score, the concordance index distribution and the refitted Cox’s proportional hazard model with the predicted average risk score as a covariate. Once we have reviewed the results we can enter the cuts we wish to make in the bar at the top. The default is a cut at the median (50). The values entered correspond to the quantiles of the cuts and show be separated by a comma (e.g.: 33,66).

Once submitted (using the submit button), the following tab Risk Group Stratification (containing the stratification results with a Kaplan-Meier and a summary table) will be updated.

The Gene View enables the user to see the selection frequency of each feature and their mean coefficients. The top bar takes names of features as input, these are simply separated by a comma as shown below. They will be printed on the volcano plot to ease the search for specific features.

Finally the Validation and Patient View tab let’s the user input a new data set with a similar set of features as shown in the sections above about prediction and validation. These tabs will return the output from those sections.